In conventional measurement while drilling “MWD”, borehole inclination and borehole azimuth are determined at a discrete number of longitudinal points along the axis of the borehole. The discrete measurements may be assembled into a survey of the well and used to calculate a three-dimensional well path (e.g., using the minimum curvature assumption). The use of accelerometers, magnetometers, and gyroscopes are well known in such conventional borehole surveying techniques for measuring borehole inclination and/or borehole azimuth. For example, borehole inclination is commonly derived from tri-axial accelerometer measurements of the earth's gravitational field. Borehole azimuth is commonly derived from a combination of tri-axial accelerometer and tri-axial magnetometer measurements of the earth's gravitational and magnetic fields.
Such static surveying measurements are generally made after drilling has temporarily stopped (e.g., when a new length of drill pipe is added to the drill string). While these static surveying measurements are often sufficient to obtain a well path of suitable accuracy, it is commonly desirable to measure the borehole inclination and borehole azimuth dynamically (i.e., in substantially real time) while drilling as such measurements provide a more timely indication of the drilling direction. Dynamic borehole inclination values may be derived from an axial accelerometer measurement and an estimate (or previous measurement) of the total gravitational field. Such dynamic inclination measurements are commonly made in commercial drilling operations, for example, using the PZIG® and iPZIG® tools available from PathFinder®, A Schlumberger Company, Katy, Tex., USA.
Methods for making dynamic borehole azimuth measurements are also known. For example, the borehole azimuth may be derived while drilling from an axial magnetic field measurement and estimates of at least two local magnetic field components, such as magnetic dip and total magnetic field. This approach and other reported methods suffer from a number of deficiencies and are therefore not commonly implemented. For example, axial magnetic field measurements are particularly sensitive to magnetic interference emanating from nearby drill string components (e.g., including the drill bit, a mud motor, a reaming tool, and the like) rendering the technique unsuitable for near-bit applications. Moreover, the accuracy of the derived azimuth is poor when the azimuth is oriented close to magnetic north or magnetic south. Other reported methods require the use of transverse accelerometer measurements, which are often contaminated by lateral vibration and centripetal acceleration components due to drill string vibration, stick/slip, whirl, and borehole wall impacts.